1. Field of the Invention
The present invention relates to an optical system using one or a plurality of optical members (lens and the like) having an uneven optical characteristics (e.g., uneven radial refractive index about an optical axis); and, in particular, to a projection optical system for projecting and transferring a pattern on a projection original onto a photosensitive substrate, or an illumination optical system for illuminating the projection original. Further, the present invention relates to a method of making a projection optical system, a method of making an illumination optical system, a method of making an exposure apparatus, an exposure method, and a method of making a micro device.
2. Related Background Art
In a step of making a semiconductor circuit device, a liquid crystal display device, or the like, an exposure apparatus is used. This exposure apparatus is an apparatus for projecting and transferring a pattern on a projection original such as reticle or mask onto a photosensitive substrate such as wafer or glass plate byway of a projection optical system. In order to project a fine mask pattern onto the photosensitive substrate, the projection optical system requires a very high optical performance in that it has a high resolution with nearly no aberration.
Hence, in order to correct the aberration resulting from a manufacturing error upon assembling the projection optical system, the thickness or the like of washers in the lens barrel for holding optical members such as lens has been changed, lens surfaces have been reground, and so forth.
For achieving a higher accuracy and larger NA in the projection optical system, the in-homogeneousness in refractive index within the lenses has been becoming a factor which is not negligible. The in-homogeneousness in refractive index within the lenses cannot be neglected in particular when there are a large number of constituent lenses.
This in-homogeneousness in refractive index within lenses cannot be corrected by changing the thickness or the like of washers or repolishing lens surfaces. Therefore, it has conventionally been impossible to make lenses from ingots of lenses which do not fall within a tolerance for use.
However, if ingots whose evenness of refractive index does not fall within the tolerance for use are discarded, then the efficiency of making lenses will decrease, thus lowering the efficiency of making projection optical systems. This problem relates to not only the making of projection optical systems, but also the making of illumination optical systems or the making of various kinds of apparatus such as inspection apparatus requiring high optical performances.
It is an object of the present invention to provide methods of making various kinds of optical systems such as projection optical systems which use one or a plurality of optical members (lens and the like) having an uneven refractive index and can secure required optical performances, and methods of making various kinds of apparatus.
In most of lenses having an uneven refractive index, the in-homogeneousness of refractive index is distributed in the radial direction, whereas the refractive index is uniform in the circumferential direction. Taking account of this point, the present invention overcomes the above-mentioned problem. Namely, it provides an optical system using one or a plurality of lenses whose radial refractive index about an optical axis is uneven, and having one or a plurality of aspheric surfaces for correcting an aberration caused by the in-homogeneousness of refractive index in the lenses. Preferably, the optical system is a projection optical system for projecting and transferring a pattern on a projection original onto a photosensitive substrate or an illumination optical system for illuminating the projection original, for example.
Thus, the present invention corrects the aberration deteriorated due to the use of lenses having an uneven refractive index distribution by employing aspheric surfaces.
Preferably, in the present invention, each of the lenses with the uneven refractive index has the following relationship:
[Expression 1]
nmaxxe2x88x92nmin greater than 1xc3x9710xe2x88x927xe2x80x83xe2x80x83(1) 
where nmax is the maximum value of refractive index, and nmin is the minimum value of refractive index. Namely, it is preferred that, if (1) is satisfied, then the lens be considered to have an uneven refractive index, and its resulting aberration be corrected by an aspheric surface.
Conversely, if the degree of in-homogeneousness in refractive index is outside of the range according to expression (1), then the refractive index distribution of the lens can be considered substantially uniform. Hence, if the aberration resulting from such a lens is to be corrected by an aspheric surface, then the difference between the aspheric surface and spherical surface (sag amount) becomes so small that it will be meaningless to introduce the aspheric surface.
Preferably, the projection optical system of the present invention is constituted, successively from the projection original side, by a first lens group having a positive refracting power, a second lens group having a negative refracting power, a third lens group having a positive refracting power, a fourth lens group having a negative refracting power, a fifth lens group having a positive refracting power, and a sixth lens group having a positive refracting power.
The first lens group having a positive refracting power mainly contributes to correction of distortion, while maintaining a telecentric property on the object side. Namely, a positive distortion is generated by the first lens group, so as to keep a balance with the negative distortion generated by the second and fourth lens groups.
The second and fourth lens groups having a negative refracting power mainly contribute to correction of Petzval sum. The second and third lens groups form an inverted Galilean system and not only adjusts magnification but also contributes to securing a back focus in the projection optical system.
The fifth and sixth lens groups having a positive refracting power contributes to restraining distortion from occurring and, in particular, to restraining spherical aberration from occurring.
In the case where the projection optical system has the six-group configuration mentioned above, it preferably satisfies:
[Expression 2]
0.04 less than |f4/L less than 0.2xe2x80x83xe2x80x83(2) 
0.02 less than f5/L less than 0.9xe2x80x83xe2x80x83(3) 
0.02 less than f6/L less than 1.5xe2x80x83xe2x80x83(4) 
D56/L less than 0.3xe2x80x83xe2x80x83(5) 
0.5 less than D6/R6 less than 1.5xe2x80x83xe2x80x83(6) 
Here,
fi is the focal length of the i-th lens group (i=4, 5, 6);
L is the distance from the object surface to the image plane on the optical axis;
D56 is the interval between the fifth and sixth lens groups;
D6 is the distance from the lens surface closest to the object in the sixth lens group to the image plane on the optical axis; and
R6 is the radius of curvature of the lens surface closest to the object in the sixth lens group on the optical axis.
Conditional expression (2) relates to the balance between spherical aberration and coma. If the lower limit of conditional expression (2) is not satisfied, then aspherical aberration is harder to correct, and it becomes further difficult to use a lens having an uneven refractive index. If its upper limit is exceeded, by contrast, then coma occurs, and it also becomes difficult to use a lens with an uneven refractive index.
Conditional expression (3) relates to a balance among spherical aberration, distortion, and Petzval sum. If the lower limit of conditional expression (3) is not satisfied, then negative distortion and negative spherical aberration enhance, and it becomes further difficult to use a lens with an uneven refractive index. If its upper limit is exceeded, by contrast, then it becomes harder to correct Petzval sum favorably, and it also becomes difficult to use a lens with an uneven refractive index.
Conditional expression (4) relates to the balance between higher-order spherical aberration and negative distortion. If the lower limit of conditional expression (4) is not satisfied, then negative distortion and negative spherical aberration enhance, and it becomes further difficult to use a lens with an uneven refractive index. If its upper limit is exceeded, by contrast, then higher-order spherical aberration occurs, and light beams pass through the lenses at acute angles, whereby it also becomes difficult to use a lens with an uneven refractive index.
If the upper limit of conditional expression (5) is exceeded, then the lens interval between the fifth and sixth lens groups increases so that not only the positive distortion is weakened, but also the influence of light beams being emitted at acute angles generates further higher-order spherical aberration or the like, which is harder to correct.
If the lower limit of conditional expression (6) is not satisfied, then the positive refracting power of the lens surface closest to the object in the sixth lens group becomes so strong that negative distortion and coma enhance, and it becomes further difficult to use a lens with an uneven refractive index. If its upper limit is exceeded, by contrast, then coma occurs greatly, and it also becomes difficult to use a lens with an uneven refractive index.
Next, when the projection optical system has the above-mentioned six-group configuration, it is preferred that at least one of a lens surface of a lens belonging to the first lens group and a lens surface of the lens disposed closest to the first lens group in the second lens group be formed by the aspheric surface and satisfy the following condition:
[Expression 3]
|Dfxe2x88x92Db| greater than 0.1xe2x80x83xe2x80x83(7) 
where
Df=Rfxc2x7sin wfxc2x7xcex/(NAxc2x7Ymax);
Db=Rbxc2x7sin wbxc2x7xcex/(NAxc2x7Ymax);
Rf is the radius of the wavefront form with respect to the maximum image height concerning a system in which the aspheric surface is replaced by a spherical surface (absolute amount of image plane incident angle);
wf is the incident azimuth of the wavefront form with respect to the maximum image height concerning the system in which the aspheric surface is replaced by a spherical surface;
Rb is the radius of the wavefront form with respect to the maximum image height concerning a system employing the aspheric surface (absolute amount of image plane incident angle);
wb is the incident azimuth of the wavefront form with respect to the maximum image height concerning the system in which the aspheric surface is employed;
xcex is the wavelength in use;
NA is the maximum numerical aperture on the image side; and
Ymax is the maximum image height.
The above-mentioned conditional expression (7) is a conditional expression for efficiently correcting various kinds of aberration deteriorated due to the use of lenses having an in-homogeneousness in refractive index. In particular, it is a conditional expression for contributing to correction of distortion by forming at least one of a lens surface of a lens belonging to the first lens group and a lens surface of the lens disposed closest to the first lens group in the second lens group into the aspheric surface.
If the lower limit of conditional expression (7) is not satisfied, then the distortion deteriorated due to the use of a lens with an in-homogeneousness in refractive index is not so deteriorated in reality, whereby it is meaningless to introduce the aspheric surface at the position mentioned above; or the distortion is not efficiently corrected though it is deteriorated to a certain extent, whereby the difference between the aspheric surface and spherical surface (sag amount) is so small that it is meaningless to introduce the aspheric surface.
Also, when the projection optical system has the above-mentioned six-group configuration, it is preferred that at least one of a lens surface of a lens belonging to the second lens group and a lens surface of the lens disposed closest to the second lens group in the third lens group be formed by the aspheric surface and satisfy the following condition:
[Expression 4]
|Afxe2x88x92Ab| greater than 0.02xe2x80x83xe2x80x83(8) 
Here,
Af=(4Rf4xe2x88x923Rf2)cos 2wfxc2x7xcex/(NAxc2x7Ymax); and
Ab=(4Rb4xe2x88x923Rb2)cos 2wbxc2x7xcex/(NAxc2x7Ymax).
The above-mentioned conditional expression (8) is a conditional expression for efficiently correcting various kinds of aberration deteriorated due to the use of lenses having an in-homogeneousness in refractive index. In particular, it is a conditional expression for contributing to correction of the fifth-order astigmatic difference by forming at least one of a lens surface of a lens belonging to the second lens group and a lens surface of the lens disposed closest to the second lens group in the third lens group into the aspheric surface.
If the lower limit of conditional expression (8) is not satisfied, then the astigmatic difference deteriorated due to the use of a lens with an in-homogeneousness in refractive index is not so deteriorated in reality, whereby it is meaningless to introduce the aspheric surface at the position mentioned above; or the astigmatic difference is not efficiently corrected though it is deteriorated to a certain extent, whereby the difference between the aspheric surface and spherical surface (sag amount) is so small that it is meaningless to introduce the aspheric surface.
Also, when the projection optical system has the above-mentioned six-group configuration, it is preferred that at least one lens surface of lenses belonging to the third and fourth lens groups be formed by the aspheric surface and satisfy the following condition:
[Expression 5]
|Cfxe2x88x92Cb| greater than 0.06xe2x80x83xe2x80x83(9) 
Here,
Cf=(10Rf5xe2x88x9212Rf3+3Rf)sin wfxc3x97xcex/(NAxc2x7Ymax); and
Cb=(10Rb5xe2x88x9212Rb3+3Rb)sin wbxc3x97xcex/(NAxc2x7Ymax).
The above-mentioned conditional expression (9) is a conditional expression for efficiently correcting various kinds of aberration deteriorated due to the use of lenses having an in-homogeneousness in refractive index. In particular, it is a conditional expression for contributing to correction of coma by forming at least one lens surface of lenses belonging to the third and fourth lens groups into the aspheric surface.
If the lower limit of conditional expression (9) is not satisfied, then the coma deteriorated due to the use of a lens with an in-homogeneousness in refractive index is not so deteriorated in reality, whereby it is meaningless to introduce the aspheric surface at the position mentioned above; or the coma is not efficiently corrected though it is deteriorated to a certain extent, whereby the difference between the aspheric surface and spherical surface (sag amount) is so small that it is meaningless to introduce the aspheric surface.
Also, when the projection optical system has the above-mentioned six-group configuration, it is preferred that at least one lens surface of lenses belonging to the fifth and sixth lens groups be formed by the aspheric surface and satisfy the following condition:
[Expression 6]
|Sfxe2x88x92Sb| greater than 0.02xe2x80x83xe2x80x83(10) 
Here,
Sf=(20Rf6xe2x88x9230Rf4+12Rf2xe2x88x921)xc2x7xcex/(NAxc2x7Ymax); and
Sb=(20Rb6xe2x88x9230Rb4+12Rb2xe2x88x921)xc2x7xcex/(NAxc2x7Ymax).
The above-mentioned conditional expression (10) is a conditional expression for efficiently correcting various kinds of aberration deteriorated due to the use of lenses having an in-homogeneousness in refractive index. In particular, it is a conditional expression for contributing to correction of the fifth-order spherical aberration by forming at least one lens surface of lenses belonging to the fifth and sixth lens groups into the aspheric surface.
If the lower limit of conditional expression (10) is not satisfied, then the spherical aberration deteriorated due to the use of a lens with an in-homogeneousness in refractive index is not so deteriorated in reality, whereby it is meaningless to introduce the aspheric surface at the position mentioned above; or the spherical aberration is not efficiently corrected though it is deteriorated to a certain extent, whereby the difference between the aspheric surface and spherical surface (sag amount) is so small that it is meaningless to introduce the aspheric surface.
Further, an object of the invention is to provide a method of making a projection optical system for projecting an image of a predetermined pattern formed on a projection original onto a photosensitive substrate, the method having: a first step of measuring an in-homogeneousness in refractive index of a plurality of dioptric optical members; a second step of calculating an aberration generated by a dioptric optical member having an in-homogeneousness in refractive index; a third step of computing an aspheric surface form which can correct the aberration calculated by the second step; a fourth step of giving the aspheric surface form computed by the third step to the dioptric optical member; and a fifth step of assembling the dioptric optical members.
Here, it is preferred that the in-homogeneousness in refractive index be a radial refractive index distribution about an optical axis, and that the aspheric surface form have rotational symmetry about the optical axis.
Further object of the present invention is to provide a method of making a projection optical system for projecting an image of a predetermined pattern formed on a projection original onto a photosensitive substrate, the method including: a first measuring step for measuring an in-homogeneousness in refractive index of a plurality of dioptric optical members; a processing step for processing the plurality of dioptric optical members after the first measuring step; a second measuring step for measuring a processed surface form of the plurality of dioptric optical members after the processing step; an assembling step for assembling the projection optical system by using the plurality of dioptric optical members after the second measuring step; a third measuring step for measuring an unnecessary optical characteristics remaining in the projection optical system after the assembling step; a computing step for computing a correction surface form concerning at least one processed surface in the plurality of dioptric optical members according to respective items of measurement information obtained by the first, second, and third measuring steps in order to correct the unnecessary optical characteristics remaining in the projection optical system; a reprocessing step for reprocessing at least one processed surface in the plurality of dioptric optical members according to information concerning the correction surface form obtained by the computing step; and a finishing step for completing the projection optical system by using a dioptric optical member reprocessed by the reprocessing step and a dioptric optical member processed by the processing step or by using a dioptric optical member reprocessed by the reprocessing step.
Further object of the present invention is to provide a method of making a projection optical system for projecting an image of a predetermined pattern formed on a projection original onto a photosensitive substrate, the method including: a first measuring step for measuring an in-homogeneousness in refractive index of a plurality of dioptric optical members; a processing step for processing the plurality of dioptric optical members after the first measuring step; a second measuring step for measuring a processed surface form ofs of the plurality of dioptric optical members after the processing step; a computing step for computing a correction surface form concerning at least one processed surface in the plurality of dioptric optical members according to respective items of measurement information obtained by the first and second measuring steps in order to correct an unnecessary optical characteristics remaining in the projection optical system which occurs due to the in-homogeneousness in refractive index of the plurality of dioptric optical members and a processing error in processed surfaces of the plurality of dioptric optical members; a reprocessing step for reprocessing at least one processed surface in the plurality of dioptric optical members according to information concerning the correction surface form obtained by the computing step; and a finishing step for completing the projection optical system by using a dioptric optical member reprocessed by the reprocessing step and a dioptric optical member processed by the processing step or by using a dioptric optical member reprocessed by the reprocessing step.
Preferably, in each of the foregoing methods of making a projection optical system, the computing step further computes the correction surface form by using optical design information of the projection optical system. Also, the computing step may compute the correction surface form by using assembling information in the assembling step.
Desirably, in each of the foregoing methods of making a projection optical system, the computing step further computes the correction surface form by using assembling information in the assembling step.
Further, an object of the present invention is to provide a method of making an exposure apparatus, the method including: a step of preparing a projection optical system made by any of the foregoing methods of making the projection optical system; a step of preparing an illumination optical system for illuminating the projection original; and a step of installing the illumination optical system and the projection optical system at predetermined positions such that the projection original is illuminated by the illumination optical system and that the image of the predetermined pattern formed on the projection original is projected onto the photosensitive substrate by the projection optical system.
More further, an object of the present invention is to provide a method of making an illumination optical system for illuminating an original in order to expose an image of a predetermined pattern formed on the original onto a photosensitive substrate, the method including: a first measuring step for measuring an in-homogeneousness in refractive index of a plurality of dioptric optical members; a processing step for processing the plurality of dioptric optical members after the first measuring step; a second measuring step for measuring a processed surface form of the plurality of dioptric optical members after the processing step; an assembling step for assembling the illumination optical system by using the plurality of dioptric optical members after the second measuring step; a third measuring step for measuring an unnecessary optical characteristics remaining in the illumination optical system after the assembling step; a computing step for computing a correction surface form concerning at least one processed surface in the plurality of dioptric optical members according to respective items of measurement information obtained by the first, second, and third measuring steps in order to correct the unnecessary optical characteristics remaining in the illumination optical system; a reprocessing step for reprocessing at least one processed surface in the plurality of dioptric optical members according to information concerning the correction surface form obtained by the computing step; and a finishing step for completing the illumination optical system by using a dioptric optical member reprocessed by the reprocessing step and a dioptric optical member processed by the processing step or by using a dioptric optical member reprocessed by the reprocessing step.
More further, an object of the present invention is to provide a method of making an illumination optical system for illuminating an original in order to expose an image of a predetermined pattern formed on the original onto a photosensitive substrate, the method including: a first measuring step for measuring an in-homogeneousness in refractive index of a plurality of dioptric optical members; a processing step for processing the plurality of dioptric optical members after the first measuring step; a second measuring step for measuring a processed surface form ofs of the plurality of dioptric optical members after the processing step; a computing step for computing a correction surface form concerning at least one processed surface in the plurality of dioptric optical members according to respective items of measurement information obtained by the first and second third measuring steps in order to correct an unnecessary optical characteristics remaining in the illumination optical system which occurs due to the in-homogeneousness in refractive index of the plurality of dioptric optical members and a processing error in processed surfaces of the plurality of dioptric optical members; a reprocessing step for reprocessing at least one processed surface in the plurality of dioptric optical members according to information concerning the correction surface form obtained by the computing step; and a finishing step for completing the illumination optical system by using a dioptric optical member reprocessed by the reprocessing step and a dioptric optical member processed by the processing step or by using a dioptric optical member reprocessed by the reprocessing step.
More further, an object of the present invention is to provide a method of making an exposure apparatus, the method including: a step of preparing an illumination optical system made by any of the foregoing methods of making the illumination optical system; a step of preparing a projection optical system for projecting the image of the pattern of the original onto the photosensitive substrate; and a step of installing the illumination optical system and the projection optical system at predetermined positions such that the original is illuminated by the illumination optical system and that the image of the predetermined pattern formed on the original is projected onto the photosensitive substrate by the projection optical system.
More further, an object of the present invention is to provide a method of making a micro device, the method including: a preparation step of preparing an exposure apparatus made by the foregoing method of making the exposure apparatus; an illumination step of illuminating the original by using the illumination optical system; an exposure step of exposing the image of the pattern of the original to the photosensitive substrate by using the projection optical system; and a development step of developing the photosensitive substrate exposed by the exposure step.